Growth of Planetary Embryos: Conserving Mass During Planet Formation in the Oligarchic Growth Stage

In order to fine-tune our current understanding of the formation of planets, we update the classic model of oligarchic growth to include mass conservation. In the early stages of planet formation, the protoplanetary disk contained only a swarm of planetesimals, rocky bodies with diameters of at most about 100 km, that collided together to form embryos greater than 1,000 km in diameter. Because planetesimals accrete, or accumulate, onto embryos, the surface mass density of the planetesimal swarm decreases with time. Here we describe surface mass density of the planetesimal swarm as the total initial surface mass density of the protoplanetary disk minus the surface mass density of the embryos. However, as the mass of the individual embryos increases, the average spacing between them must also change. Therefore, the parameter that is related to the characteristic spacing between embryos, b, must also change. We incorporate the changing eccentricity and surface mass density into a model that describes the growth of any given planetary embryo in the protoplanetary disk, which includes the new formulation for mass conservation. Finally, we test how the presence of a circum-embryo debris disk affects the growth rate of a planet. Because a debris disk in orbit about an embryo will increase the collisional cross-section of the planetary embryo, the time needed to fully grow the embryo decreases. The accelerated growth rate due to the circum-embryo disk holds implications for describing the formation of gas giant cores within the necessary timescale to capture the gas from the surrounding protoplanetary disk